Best Known (65, 65+59, s)-Nets in Base 2
(65, 65+59, 43)-Net over F2 — Constructive and digital
Digital (65, 124, 43)-net over F2, using
- t-expansion [i] based on digital (59, 124, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(65, 65+59, 48)-Net over F2 — Digital
Digital (65, 124, 48)-net over F2, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 65 and N(F) ≥ 48, using
(65, 65+59, 149)-Net in Base 2 — Upper bound on s
There is no (65, 124, 150)-net in base 2, because
- 1 times m-reduction [i] would yield (65, 123, 150)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2123, 150, S2, 58), but
- the linear programming bound shows that M ≥ 36000 467012 365704 432940 148948 904738 978722 217984 / 3201 323125 > 2123 [i]
- extracting embedded orthogonal array [i] would yield OA(2123, 150, S2, 58), but